Problem: What do the following two equations represent? $-3x-y = 2$ $x-3y = 3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x-y = 2$ $-y = 3x+2$ $y = -3x - 2$ Putting the second equation in $y = mx + b$ form gives: $x-3y = 3$ $-3y = -x+3$ $y = \dfrac{1}{3}x - 1$ The slopes are negative inverses of each other, so the lines are perpendicular.